GPU finite element method computation strategy without mesh coloring

Abstract

A GPU-adapted Finite Element Method (A-FEM) implementation without using a mesh coloring strategy to avoid race conditions is presented. All the elements are simultaneously processed, and the local data is computed and consolidated into the device memory in a new adapted Coordinate Format data structure (a-COO). The comparison between the proposed solution and two GPU Element-by-Element Finite Element Method (EbE-FEM) approaches shows promising results since it is no longer necessary the mesh coloring step. This new approach is well suited for problems that need re-meshing and consequently would need re-coloring, e.g., adaptive mesh refinement.